Faraday's Law states that a changing magnetic field through a closed curve will induce an electric field that is proportional to the magnetic field's rate of change. Maxwell's modification of Ampere's Law states that a changing electric field through a closed surface will induce a magnetic field that is proportional to the electric field's rate of change. This amazing set of symmetric dependencies indicates that an electromagnetic wave, once initiated, would be self-propagating.

Although the actual derivation is beyond the scope and mathematics of this introductory course, when Maxwell combined these equations he discovered a wave equation for the electric and magnetic field vectors. In 1886, Maxwell postulated that his waves could be generated by accelerating electric charges and that they would travel at a speed equal to the speed of light.
This extraordinary result would prove to be the unifying link between electricity and light.